Sorry bad news here. As you may have already realized some of the roads in Poland are not yet in very good condition and hundreds of kilometers are being reconstructed and renovated. Just a year or two of patience. In Warsaw we are in the middle of an extensive program of road building and reconstruction. There is extensive work on a Warsaw by-pass as well as new connections to Warsaw being built together with the highway that will finally connect the Capital City with Europe. We still hope it will happen before EURO 2012 TM. What is more the construction of a second Metro line was started in October 2010 to be finished in 2013. All this will cause serious traffic jams with many important city centre streets closed.
There are big traffic jams on the roads leading to the city centre during the morning and afternoon rush hours. Public transport gets stuck as well but today there are more and more priority lanes for buses and this helps a lot. The best solution is the tramway system as the majority of the lines are separate from the private/public transport lanes.
If you decide to explore Warsaw by car follow the big red-blue signs. These indicate the areas of the city. The Palace of Culture still seems to be the best orientation landmark as you can see it from all parts of the city. Remember that the speed limit in the city is 50 km/h and some Polish drivers respect it. A little warning, there are an increasing amount of speed cameras in the city, and more are on their way. So Be Cool. Drive Safely.